On 01 Oct 2015, at 22:09, John Clark wrote:
On Thu, Oct 1, 2015 at 12:01 PM, Bruno Marchal <[email protected]>
wrote:
>> When I say "physical computation" and you demand a
definition of that and when I respond with "a computation done with
physics" and you demand a definition of that too then I believe it
is perfectly acceptable for me to either get off the silly
definition merry-go-round or to demand a definition of my own, a
definition of definition.
> But this distracts us from what we should focus on.
I agree it's a silly waste of time, so why did you demand
a definition of physical computation?
Because you seem to doubt that the existence of computation in
arithmetic. But your argument relies on a notion of physical
computation. When I ask what that is, your definition seems to be
"implementation of computation (in the arithmetical sense) in a
physical reality, which contradicts your statement that computation
does not exist in arithmetic.
> A computation can be defined by what universal machines do.
But that universal machine can't do a
damn thing without the help of physics, therefore your
definition is unimportant.
It cannot do a damn thing in the physical reality indeed.
But that is not relevant to the fact that it can do a lot of thing in
arithmetic, and indeed, eventually we show that the physical
computations emerge as a first person plural views of the machine
emulated in arithmetic.
> A universal machine is defined by a number u such that
phi_u(x, y) = phi_x(y).
You can define it however you like, but if that machine
isn't made of matter that obeys the laws of physics it's not
going to be doing any calculations, and it's not going to be doing
anything else either.
This is simply wrong, and I think it means you persist in confusing
what is a computation in the CHurch-Turing sense, which does not
assume anything physical, and an implementation of such a machine in a
physical reality. In the context of the mind-body problem, that is a
crucial difference that we have to take into account.
> None of those theories assume anything material.
And none of those theories can perform calculations, no theory can,
Actually theory are not necessarily supposed to be able to do that,
only machine (in the mathematical sense) can do that. Now, it happens
that if a theory is sigma_1 complete, like RA and PA, they can do
that, because such theories are universal machine (again in the Turing
sense).
only physical material can do that.
Physical material can do that in the physical world, but here we talk
about the computation done in arithmetic. obviously, we cannot use
them in any direct way, like we can do with a physical machine. That
does not change the fact that a tiny part of the arithmetical truth
can emulate some computation (indeed all of them).
>> you use the term computation in the sense of Church-Turing.
>> I use the term "computation" in the sense of actually
finding a particular solution to a particular problem in arithmetic;
and neither Church nor Turing were fools so they meant the same thing.
> Come on! You are the guy which pretend to accept
computationalisme.
Why on earth would I pretend to accept computationalism if I did not?
Not only you accept comp, but you have often argued that we need to be
stupid to not accept it. Actually, you are even someone saying yes to
a doctor. All your post illustrates that you are a sort of comp
believer. Comp is put for computationalism.
>> A Turing Machine is physical,
> Absolutely not. Turing made it looking like that because he wanted
to capture the essence of what a human does when he compute a
function with pencil and paper.
Turing wanted to capture the essence of what ANYTHING does when a
calculation is actually made; not talked about, not theorized, not
defined, but actually MADE.
Not at all. Please read Turing before ascribing things that he never
said.
That computations exist in arithmetic (even in the small sigma_1
complete part) is accepted by all experts in the field. There is
absolutely no controverse about that. I have even been asled to
suppress the explanation of this in my french Phd thesis (to avoid the
beligian critics that I explain too much elementary material known by
everybody).
> he gave a purely mathematical definition
That's nice, but defining a calculation and making a calculation
is not the same thing,
Of course. But once Turing defined calculation/computation, it has
been proved that it exists in any model of arithmetic, a fortiori in
the standard model.
just as "a fast red car" is NOT a fast red car. Definitions
can't make calculations, only matter that obeys the laws of physics
can do that.
Not at all. You need a physical reality only to implement a physical
computation. But that is trivial, because a physical computation is
the implementation in a physical reality of a mathematical
(arithmetical) computation.
>> there is ZERO evidence that arithmetic can calculate anything
without the help of physics
> Zero evidences enough when we prove a theorem!
But that is not nearly enough if you want to know a particular
solution to a particular problem in arithmetic because neither
proofs nor theorems can make a calculation; for that you need physics.
Yes, but it happens that we are not interested in having a solution,
but only in their existence, to procede in the reasoning.
>> as of September 30 2015 every calculation ever observed has
involved matter that obeys the laws of physics. No exceptions, not a
single one.
> But I am not talking about the computations that we (perhaps)
observe. I am talking about the computations which exist in
arithmetic.
So you're talking about computations that no machine and no person
has ever performed or even observed, and calculations for which
there is no evidence that they exist at all.
They exist in the same sense that a prime number bigger than
1000^(1000^1000) exists, By the invariance of the first person
experiences for the Universal Dovetailing delays (measured in number
of calculation step), the fact that we can't realize those
computations physically is not relevant.
You have not answered my question (probably because you refuse the
standard definition of computation and digital machines). How could a
universal Turing machine makes the difference between an
implementation in arithmetic and an implementation in a physical
reality?
Bruno
John K Clark
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